It came as Barack Obama said that the siege of thousands of desperate refugees trapped by Islamic State extremists in Iraq had been “broken”, after it emerged on Thursday that only a “few hundred” remain on Mount Sinjar.

Mr Obama said that aid drops to refugees on the mountain would stop and US military advisers would pull out.

Mr Cameron hailed the changed situation as “good news”, as plans to use British Chinook helicopters and Tornado fighter jets in a rescue operation were put on hold. Humanitarian aid drops on the mountain will also end.

Meanwhile, Britain’s most senior police officer warned that hundreds of British jihadists could return to Britain and pose a threat to national security if Islamic State loses battles in Iraq and Syria.

Bernard Hogan-Howe, the head of the Metropolitan Police, said the return of the jihadists was his “biggest concern” and that they would put “great pressure” on police and security services.

Despite the improved situation in the north, Islamic State militants continued to make progress in other parts of the country, moving closer to Baghdad.

The United Nations said Iraq still faced a “level 3” crisis – the most serious possible – with some 200,000 people estimated to have been displaced by the militants’ advance.

The Archbishop of Canterbury yesterday urged the international community to document atrocities in northern Iraq so the perpetrators could be brought to justice.

The Most Rev Justin Welby said the human rights abuses perpetrated against Christians and other minorities, which have included beheadings and crucifixions, are “off the scale of human horror”.

Mr Obama said the situation elsewhere in Iraq remains dire, as both he and Mr Cameron announced plans to bolster aid efforts in refugee camps. British Tornados and Chinooks will remain in the region.

Mr Cameron said: “It is very difficult in an area where you have got a lot of fighting taking place, you have got a lot of people moving around.

“So what you need to do is have plans that are flexible enough to respond to that situation. It is important to get the assets into place. That is why the Chinooks are there, that’s why our Tornados are there.”

The Telegraph has learnt that Mr Cameron announced on Wednesday that he was prepared to push ahead with a rescue operation despite concerns within the Army.

According to military sources, he was warned that a corridor for Kurds to escape could not have been established without ground troops, and that every time a helicopter airlifted refugees it would have been at risk.

Labour’s Ann Clwyd, a former special envoy on Iraq to Tony Blair and Gordon Brown, claimed that Mr Cameron’s refusal to recall Parliament to discuss the crisis was an attempt to “gag” MPs.

At a briefing with journalists, Mr Hogan-Howe warned of the “large numbers” of jihadists who could soon return to Britain. “The biggest concern certainly I have is that none of us know which way those wars are going to go,” he said.

“We’ve seen some quite radical movements across whole countries. Look at Iraq, the shift in a few days. These world events were moving at pace.

“That was obviously Islamists who were progressing positively. If there were to be a reverse of that at pace, and they were to lose, there is a risk that hundreds of people would want to come home.

“That’s the biggest challenge. We can’t predict when it might happen. Should there be large numbers returning it puts great pressure on all of us to make sure that we are kept safe.”

Kurdish forces told The Telegraph that few people remain on the mountain, although hundreds are dead.

Abdul Rahman Hemo, of the YPG, the Syrian Kurdish armed forces who have secured the parts of Mount Sinjar inhabited by the refugees, said: “Yesterday there were still more than 1,000 people on the mountain. Today there are just a few hundred.”

Dr Hussein al-Azzam, who heads the Nawrooz refugee camp in Syria, the first place of rest for the refugees from Sinjar, said the fact that few were left on the mountain was to be celebrated but warned that the humanitarian crises was “only just beginning”.